A Review of Tubular Conical Transition Strength Design Equations

2020 ◽  
Author(s):  
Albert Ku ◽  
Jieyan Chen ◽  
Bernard Cyprian
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Yield Criterion ◽  
Plasticity Theory ◽  
Transition Strength ◽  
Ultimate Capacity ◽  
Design Standards ◽  
Fem Simulations ◽  
Column Type ◽  
Shell Equations

Abstract This paper consists of two parts. Part one presents a thin-shell analytical solution for calculating the conical transition junction loads. Design equations as contained in the current offshore standards are based on Boardman’s 1940s papers with beam-column type of solutions. Recently, Lotsberg presented a solution based on shell theory, in which both the tubular and the cone were treated with cylindrical shell equations. The new solution as presented in this paper is based on both cylindrical and conical shell theories. Accuracies of these various derivations will be compared and checked against FEM simulations. Part 2 of this paper is concerned with the ultimate capacity equations of conical transitions. This is motivated by the authors’ desire to unify the apparent differences among the API 2A, ISO 19902 and NORSOK design standards. It will be shown that the NORSOK provisions are equivalent to the Tresca yield criterion as derived from shell plasticity theory. API 2A provisions are demonstrated to piecewise-linearly approximate this Tresca yield surface with reasonable consistency. The 2007 edition of ISO 19902 will be shown to be too conservative when compared to these other two design standards.

Recommended Stress Formulae for Tubular Conical Transition Designs

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Albert Ku ◽  
Jieyan Chen
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Shell Theory ◽  
Plate Thickness ◽  
Design Standards ◽  
Shell Equations ◽  
Offshore Industry ◽  
Hoop Stresses ◽  
Code Provisions

Abstract For the design of tubular conical transitions, the axial, bending, and hoop stresses at the junctions are required. Among the offshore design standards, API RP-2A, ISO 19902, and NORSOK N-004, various equations exist for the same stress quantity which may cause confusions. The quality of these existing stress formulae will be examined in this paper. The tubular conical stress equations used in the offshore industry started from Boardman’s studies in the 1940s. Recently, Lotsberg re-formulated this problem and applied the results to stress concentration factor (SCF) applications. This paper solves the same set of shell equations but the formulations are cast in a different form. This new format allows for an in-depth examination of existing code equations. In addition, the formulation as presented can be used for modifications to gain higher accuracy. Several recommended new stress formulae are provided. It is observed that the existing code provisions’ accuracy quickly deteriorates for cases where plate thickness in tubular and cone differ. The recommended approach is based on theoretical framework of shell mechanics, which better facilitate tubular/cone force balances when compared with existing equations. The sectional relationships among moment, shear, and hoop loads are also treated consistently using shell theory. The resulted improvements make the recommended formulae more accurate than the existing provisions.

Turbulence-Induced Vibration Analysis of an Open Curved Thin Shell

2010 ◽  
Author(s):  
Mitra Esmailzadeh ◽  
Aouni A. Lakis
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Root Mean Square ◽  
Thin Shell ◽  
Shell Theory ◽  
Pressure Field ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Cross Spectral Density ◽  
Thin Shell Theory

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of the structure in terms of the cross-spectral density of random pressure fields. The cross-spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis et al.

A NEW KIND OF SINGULAR STIFF PROBLEMS AND APPLICATION TO THIN ELASTIC SHELLS

1995 ◽  
Vol 05 (01) ◽  
pp. 47-66 ◽  
Author(s):  
D. CAILLERIE ◽  
E. SANCHEZ-PALENCIA
Keyword(s):  
Asymptotic Behavior ◽  
Local Structure ◽  
Thin Shell ◽  
Spectral Properties ◽  
Shell Theory ◽  
Stiff Problems ◽  
Medium Frequency ◽  
Limit Solution ◽  
General Configuration ◽  
Thin Shell Theory

We consider the asymptotic behavior of the solution of a class of problems involving a small parameter ε and ε2. This generalizes the “singular stiff” problems arising in classical thin shell theory. The new problems appear in theory of composite shells, when the local structure implies coupling between membrane stresses and flexions. According to specific hypotheses, this kind of problems contains singular perturbations and penalty problems where the limit solution belongs to a subspace G1 of the general configuration space V. In addition to the coercive problem, spectral properties are considered in the small and medium frequency ranges, including spectral families in the case without compactness.

Free vibration of bi-material cylindrical shells

2016 ◽  
Vol 230 (15) ◽  
pp. 2637-2649 ◽  
Author(s):  
Saeed Sarkheil ◽  
Mahmud S Foumani ◽  
Hossein M Navazi
Keyword(s):  
Exact Solution ◽  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Thin Shell ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Space Technique ◽  
Thin Shell Theory

Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.

Vibration of Shallow Shells: A Review With Bibliography

1997 ◽  
Vol 50 (8) ◽  
pp. 431-444 ◽  
Author(s):  
K. M. Liew ◽  
C. W. Lim ◽  
S. Kitipornchai
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Free Vibration Analysis ◽  
Review Article ◽  
Shallow Shells ◽  
First Order ◽  
Recent Developments ◽  
Thick Shells ◽  
Thin Shell Theory ◽  
Introductory Review

This review article documents recent developments in the free vibration analysis of thin, moderately thick, and thick shallow shells. An introductory review of the studies in Kirchhoff-Love classical thin shell theory is given. The development of studies in moderately thick shells incorporating the effects of transverse shear deformation and rotary inertia is detailed. This review article mainly focuses on research advances in vibration studies since the 1970s using the classical Kirchhoff-Love, first-order, and higher-order theories. The validity and range of applicability of these theories are examined. There are 163 references listed at the end of the article.

scholarly journals Calculation method of locking torque based on elastic thin shell theory for hydraulic locking sleeve

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769269
Author(s):  
Ming Yan ◽  
Hai-Chao Liu
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Calculation Model ◽  
Thin Cylindrical Shell ◽  
Deformation Equation ◽  
Test Platform ◽  
Large Elastic Deformation ◽  
Five Axis ◽  
Thin Shell Theory ◽  
Rotational Freedom

The hydraulic locking sleeve is a key component of precision instruments such as five-axis machine tools, giant astronomical telescope, and satellite antenna. This is subjected to the action of pressure load causing large elastic deformation and locking the rotational freedom of feed shaft at any angle. The maximum locking torque is an important parameter for designing the hydraulic locking sleeve. First, the hydraulic locking sleeve is simplified as elastic thin cylindrical shell structure. Neglecting the bending and twisting effects, the calculation equations describing the deformation and stress state between the hydraulic locking sleeve and rotary shaft are derived by applying the theory of elastic thin shell. Then, taking into account that one end of the hydraulic lock sleeve is fixed to the shaft sleeve seat by the end face flange; the calculating formula of the maximum locking torque of the hydraulic locking sleeve is obtained by modifying the deformation equation based on moment model. Finally, a test platform of hydraulic locking sleeve is designed, which can measure the maximum locking torque of the hydraulic locking sleeve. The error between the calculation result of locking torque theoretical calculation model and the experimental measured value is <15%. As a result, the causes of the error are analyzed, and the effects of the shaft sleeve length, wall thickness, and radius on the maximum locking torque are calculated.

scholarly journals Approximation of Linear Elastic Shells by Curved Triangular Finite Elements Based on Elastic Thick Shells Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Joseph Nkongho Anyi ◽  
Robert Nzengwa ◽  
Jean Chills Amba ◽  
Claude Valery Abbe Ngayihi
Keyword(s):  
Thin Shell ◽  
Thick Shell ◽  
Absolute Value ◽  
Linear Elastic ◽  
Limit Value ◽  
Shell Equations ◽  
Third Fundamental Form ◽  
Nodal Displacements ◽  
Thick Shells ◽  
Thin Shell Theory

We have developed a curved finite element for a cylindrical thick shell based on the thick shell equations established in 1999 by Nzengwa and Tagne (N-T). The displacement field of the shell is interpolated from nodal displacements only and strains assumption. Numerical results on a cylindrical thin shell are compared with those of other well-known benchmarks with satisfaction. Convergence is rapidly obtained with very few elements. A scaling was processed on the cylindrical thin shell by increasing the ratioχ=h/2R(half the thickness over the smallest radius in absolute value) and comparing results with those obtained with the classical Kirchhoff-Love thin shell theory; it appears that results diverge at2χ=1/10=0.316because of the significant energy contribution of the change of the third fundamental form found in N-T model. This limit value of the thickness ratio which characterizes the limit between thin and thick cylindrical shells differs from the ratio 0.4 proposed by Leissa and 0.5 proposed by Narita and Leissa.

A Study on Gas Pressure for Superplastic Forming of Titanium Alloy Bellows

2005 ◽  
Vol 475-479 ◽  
pp. 3051-3054 ◽  
Author(s):  
Gang Wang ◽  
Jun Chen ◽  
X.Y. Ruan
Keyword(s):  
Titanium Alloy ◽  
Thin Shell ◽  
Deformation Theory ◽  
Shell Theory ◽  
Superplastic Forming ◽  
Gas Pressure ◽  
Forming Process ◽  
Compressive Axial Load ◽  
Thin Shell Theory ◽  
Gas Pressures

The complex superplastic forming (SPF) technology applying gas pressure and compressive axial load is an advanced forming method for bellows made of titanium alloy, which forming process consists of the three main forming phases namely bulging, clamping and calibrating phase. The influence of forming gas pressure in various phases on the forming process are analyzed and models of forming gas pressure for bellows made of titanium alloy are derived according to the thin shell theory and plasticity deformation theory. Using model values, taking a two-convolution DN250 bellows made of Ti-6Al-4V titanium alloy as an example, a series of superplastic forming tests are performed to evaluate the influence of the variation of forming gas pressure on the forming process. According to the experimental results models are corrected to make the forming gas pressures prediction more accurate.

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